The 3-D viewpoint generation and information prediction steps run after the occupancy prediction stage. Inspired by [1]}, we design a two-stage approach to sample viewpoints \(VP_{i}=\lbrace (\mathbf {p}_{i,1}, \xi _{i,1}, g_{i,1}), (\mathbf {p}_{i,2}, \xi _{i,2}, g_{i, 2}), \ldots (\mathbf {p}_{i,n}, \xi _{i,n}, g_{i,n}) \rbrace \)  at each \(F_{i}\) , where \((\mathbf {p}_{i,j}, \xi _{i,j}, g_{i,j})\)  represents the 3-D position, yaw angle, and predicted information gain at each sampled viewpoint, respectively. As shown in Fig. REF , in the first stage, the position \(\mathbf {p}_{i,j}\)  of each viewpoint is uniformly sampled from the cylindrical coordinates that originate from the center of the cluster. At the second stage, centered along the line connects \(\mathbf {p}_{i,j}\)  to the center of the cluster, multiple yaw angles \(\lbrace \xi _{i,j,1}, \xi _{i,j,2}, \ldots \xi _{i,j,m}\rbrace \)  are uniformly sampled. Then, we use the methods from [2]} to avoid repeated ray-castings and compute in parallel the information gain prediction for all yaw angles sampled. The information prediction process is illustrated in Fig. REF . To reduce redundant computations, we calculate the information gain along each slice and aggregate the gains inside each FOV to get the predicted information at different sampled yaw angles. We designed a new information prediction approach by checking voxels from both the current map and the predicted map to better predict the information during ray-casting, as detailed in Algorithm REF . After predicting the information gain \(g_{i,j,k}\)  at each yaw angle \(\xi _{i, j, k}\) , we save the one with the highest information gain as \(\xi _{i,j}\)  together with \(\mathbf {p}_{i, j}\)  and \(g_{i,j}\) . At the end of the viewpoint generation process, we sort all viewpoints in descending order of predicted information and save the top \(N_{vp}\)  viewpoints to maximize utility during the planning process.
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